NEET Sample Paper NEET Sample Test Paper-21

  • question_answer A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2:1. The ratio of their nuclear sizes will be:

    A) \[{{2}^{\frac{1}{3}}}:1\]               

    B) \[1:{{3}^{\frac{1}{2}}}\]   

    C)   \[{{3}^{\frac{1}{3}}}:1\]   

    D)   \[1:{{2}^{\frac{1}{3}}}\]                           

    Correct Answer: D

    Solution :

    According to the law of conservation of momentum \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{v}_{2}}}{{{v}_{1}}}=\frac{1}{2}\] Since, masses are directly proportional to volume as densities are roughly same, so it follows that:             \[\frac{{{m}_{1}}}{{{m}_{2}}}\propto \frac{r_{1}^{3}}{r_{2}^{3}}\]or \[\frac{{{r}_{1}}}{{{r}_{2}}}\propto {{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{\frac{1}{3}}}\] \[\therefore \]ratio of nuclear sizes\[=\frac{1}{{{2}^{1/3}}}.\] Hence, the correction option is (d).


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